Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model

We combine the Density Matrix Technique (DMRG) with Green Function Monte Carlo (GFMC) simulations. The DMRG is most successful in 1-dimensional systems and can only be extended to 2-dimensional systems for strips of limited width. GFMC is not restricted to low dimensions but is limited by the efficiency of the sampling. This limitation is crucial when the system exhibits a so-called sign problem, which on the other hand is not a particular obstacle for the DMRG. We show how to combine the virtues of both methods by using a DMRG wavefunction as guiding wave function for the GFMC. This requires a special representation of the DMRG wavefunction to make the simulations possible within reasonable computational time. As a test case we apply the method to the 2-dimensional frustrated Heisenberg antiferromagnet. By supplementing the branching in GFMC with Stochastic Reconfiguration (SR) we get a stable simulation with a small variance also in the region where the fluctuations due to minus sign problem are maximal. The sensitivity of the results to the choice of the guiding wavefunction is extensively investigated. We analyse the model as a function of the ratio of the next-nearest to nearest neighbor coupling strength. We observe in the frustrated regime a pattern of the spin correlations which is in-between dimerlike and plaquette type ordering, states that have recently been suggested. It is a state with strong dimerization in one direction and weaker dimerization in the perpendicular direction.Comment: slightly revised version with added reference

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Spectropolarimetry of the Deep Impact target comet 9P/Tempel 1 with HiVIS

High resolution spectropolarimetry of the Deep Impact target, comet 9P/ Tempel 1, was performed during the impact event on July 4th, 2005 with the HiVIS Spectropolarimeter and the AEOS 3.67m telescope on Haleakala, Maui. We observed atypical polarization spectra that changed significantly in the few hours after the impact. The polarization of scattered light as a function of wavelength is very sensitive to the size and composition (complex refractive index) of the scattering particles as well as the scattering geometry. As opposed to most observations of cometary dust, which show an increase in the linear polarization with the wavelength (at least in the visible domain and for phase angles greater than about 30%, a red polarization spectrum) observations of 9P/Tempel 1 at a phase angle of 41 degrees beginning 8 minutes after impact and centered at 6:30UT showed a polarization of 4% at 650 nm falling to 3% at 950 nm. The next observation, centered an hour later showed a polarization of 7% at 650 nm falling to 2% at 950nm. This corresponds to a spectropolarimetric gradient, or slope, of -0.9% per 1000 Angstroms 40 minutes after impact, decreasing to a slope of -2.3% per 1000 Angstroms an hour and a half after impact. This is an atypical blue polarization slope, which became more blue 1 hour after impact. The polarization values of 4% and 7% at 650nm are typical for comets at this scattering angle, whereas the low polarization of 2% and 3% at 950nm is not. We compare observations of comet 9P/Tempel 1 to that of a typical comet, C/2004 Machholz, at a phase angle of 30 degrees which showed a typical red slope, rising from 2% at 650nm to 3% at 950nm in two different observations (+1.0 and +0.9% per 1000 Angstroms).Comment: Icarus Deep Impact special issue, accepted Aug 28 200

Superconducting and pseudogap phases from scaling near a Van Hove singularity

We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.Comment: 4 pages, 6 Postscript figures, the physical discussion of the results has been clarifie

A trapped-ion local field probe

We introduce a measurement scheme that utilizes a single ion as a local field probe. The ion is confined in a segmented Paul trap and shuttled around to reach different probing sites. By the use of a single atom probe, it becomes possible characterizing fields with spatial resolution of a few nm within an extensive region of millimeters. We demonstrate the scheme by accurately investigating the electric fields providing the confinement for the ion. For this we present all theoretical and practical methods necessary to generate these potentials. We find sub-percent agreement between measured and calculated electric field values

Electronic susceptibilities in systems with anisotropic Fermi surfaces

The low temperature dependence of the spin and charge susceptibilities of an anisotropic electron system in two dimensions is analyzed. It is shown that the presence of inflection points at the Fermi surface leads, generically, to a $T \log T$ dependence, and a more singular behavior, $\chi \sim T ^{3/4} \log T$, is also possible. Applications to quasi two-dimensional materials are discussed.Comment: 8 pages, 5 figures, revtex 4 styl

Charge and spin order in one-dimensional electron systems with long-range Coulomb interactions

We study a system of electrons interacting through long--range Coulomb forces on a one--dimensional lattice, by means of a variational ansatz which is the strong--coupling counterpart of the Gutzwiller wave function. Our aim is to describe the quantum analogue of Hubbard's classical ``generalized Wigner crystal''. We first analyse charge ordering in a system of spinless fermions, with particular attention to the effects of lattice commensurability. We argue that for a general (rational) number of electrons per site $n$ there are three regimes, depending on the relative strength $V$ of the long--range Coulomb interaction (as compared to the hopping amplitude $t$). For very large $V$ the quantum ground state differs little from Hubbard's classical solution, for intermediate to large values of $V$ we recover essentially the Wigner crystal of the continuum model, and for small $V$ the charge modulation amounts to a small--amplitude charge--density wave. We then include the spin degrees of freedom and show that in the Wigner crystal regimes (i.e. for large $V$) they are coupled by an antiferromagnetic kinetic exchange $J$, which turns out to be smaller than the energy scale governing the charge degrees of freedom. Our results shed new light on the insulating phases of organic quasi--1D compounds where the long--range part of the interaction is unscreened, and magnetic and charge orderings coexist at low temperatures.Comment: 11 pages, 7 figures, accepted for publication on Phys. Rev.

An Exact Diagonalization Demonstration of Incommensurability and Rigid Band Filling for N Holes in the t-J Model

We have calculated S(q) and the single particle distribution function for N holes in the t - J model on a non--square sqrt{8} X sqrt{32} 16--site lattice with periodic boundary conditions; we justify the use of this lattice in compariosn to those of having the full square symmetry of the bulk. This new cluster has a high density of vec k points along the diagonal of reciprocal space, viz. along k = (k,k). The results clearly demonstrate that when the single hole problem has a ground state with a system momentum of vec k = (pi/2,pi/2), the resulting ground state for N holes involves a shift of the peak of the system's structure factor away from the antiferromagnetic state. This shift effectively increases continuously with N. When the single hole problem has a ground state with a momentum that is not equal to k = (pi/2,pi/2), then the above--mentioned incommensurability for N holes is not found. The results for the incommensurate ground states can be understood in terms of rigid--band filling: the effective occupation of the single hole k = (pi/2,pi/2) states is demonstrated by the evaluation of the single particle momentum distribution function . Unlike many previous studies, we show that for the many hole ground state the occupied momentum states are indeed k = (+/- pi/2,+/- pi/2) states.Comment: Revtex 3.0; 23 pages, 1 table, and 13 figures, all include

Marine litter

The results from the various investigations and monitoring programmes presented in this report demonstrate the continuous and widespread occurrence of litter in the Wadden Sea and adjacent offshore waters. Marine litter of different sizes and from diverse sources occurs on dunes and beaches, in and on inter- to subtidal sediments and in marine organisms, including protected seabirds and mammals. The OSPAR Beach Litter Monitoring and Monitoring on Litter in Fulmars’ Stomachs provide an evaluation of the temporal development of litter abundance in the southern North Sea. Both programmes clearly show that litter densities have not declined since the last Wadden Sea QSR in 2009, indicating that large amounts of litter are still entering the marine environment either directly within the Wadden Sea or from adjacent waters. The amount of litter entering the marine environment is continuously increasing(Jambeck et al., 2015). This increase is, however, not apparent in the results of the two monitoring programmes. Litter degrades in the marine environment and breaks down into ever smaller fragments. The fragmentation of plastic objects produces microplastics, which are not sufficiently assessed by current monitoring programmes. Densities of microplastics are expected to increase substantially in the future in all marine habitats. Accordingly, scientifically sound monitoring of these synthetic particles with standardized methods that allow for the comparison of results from different programmes will be indispensable.Marine litter is not restricted to specific habitats but occurs in all compartments of the marine environment with a constant exchange between them. Accordingly, monitoring litter densities in both coastal and offshore habitats is essential for a sound evaluation of litter pollution of the Wadden Sea. Many of the investigations presented in this report are on-off events, which do not provide information on temporal trends. However, they do demonstrate that the Wadden Sea is contaminated with marine litter and that litter densities in the Wadden Sea are not lower than in other coastal regions. The litter densities presented in this report provide a valuable baseline for future evaluations of temporal trends. The monitoring of litter in fulmars’ stomachs and the examinations of carcasses of harbour porpoise, harbour seals and eider ducks revealed that litter does not simply occur in the marine environment but actually interacts in a potentially harmful way with the marine biota. It is well established that the ingestion of litter can have deleterious and often lethal effects on marine organisms. It is yet unknown whether marine litter has demographically relevant implications for marine species. For evaluating this, the effects of marine litter must not be considered in isolation but always together with the effects of other environmental stressors such as ocean warming and acidification, eutrophication and the exploitation of natural stocks (see reports on climate change, geomorphology, eutrophication and fisheries). SeveralWadden Sea Plan targets are compromised by the continuous pollution of the North Sea with marine litter. A proper management of the marine litter problem will require appropriate reduction measures and extended and optimized monitoring programmes in order to evaluate future developments